Q. 2 A5.0( 2 Votes )

# Solve the following system of equations by matrix method:x + y –z = 32x + 3y + z = 103x – y – 7z = 1

The given system can be written in matrix form as: or A X = B

A = , X = and B = Now, |A| = 1 = (– 20) – 1(– 17) – 1(11)

= – 20 + 17 + 11 = 8

So, the above system has a unique solution, given by

X = A – 1B

Cofactors of A are:

C11 = (– 1)1 + 1 – 21 + 1 = – 20

C21 = (– 1)2 + 1 – 7 – 1 = 8

C31 = (– 1)3 + 1 1 + 3 = 4

C12 = (– 1)1 + 2 – 14 – 3 = 17

C22 = (– 1)2 + 1 – 7 + 3 = – 4

C32 = (– 1)3 + 1 1 + 2 = – 3

C13 = (– 1)1 + 2 – 2 – 9 = – 11

C23 = (– 1)2 + 1 – 1 – 3 = 4

C33 = (– 1)3 + 1 3 – 2 = 1

adj A = = Now, X = A – 1B = X = X = Hence, X = 3,Y = 1 and Z = 1

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